System object: phased.IsotropicProjector
Plot isotropic projector directivity and patterns
[PAT,AZ_ANG,EL_ANG] = pattern(___)
the 3D directivity pattern (in dBi) for the projector specified in
The operating frequency is specified in
the projector pattern with additional options specified by one or
Name,Value pair arguments.
returns the projector pattern in
[PAT,AZ_ANG,EL_ANG] = pattern(___)
contains the coordinate values corresponding to the rows of
EL_ANG output contains the coordinate values
corresponding to the columns of
PAT. If the
is set to
the U coordinates of the pattern and
the V coordinates of the pattern. Otherwise, they
are in angular units in degrees. UV units are dimensionless.
comma-separated pairs of
the argument name and
Value is the corresponding value.
Name must appear inside quotes. You can specify several name and value
pair arguments in any order as
Examine the response and patterns of an isotropic projector operating between 1 kHz and 10 kHz.
Set the projector parameters and obtain the voltage response at five different elevation angles: -30°, -15°, 0°, 15° and 30°. All elevation angles at 0° azimuth angle. The voltage response is computed at 2 kHz.
projector = phased.IsotropicProjector('FrequencyRange',[1,10]*1e3); fc = 2e3; resp = projector(fc,[0,0,0,0,0;-30,-15,0,15,30]);
Draw a 3-D plot of the voltage response.
pattern(projector,fc,[-180:180],[-90:90],'CoordinateSystem','polar', ... 'Type','power')
Examine the response and patterns of an isotropic projector at three different frequencies. The projector operates between 1 kHz and 10 kHz. Specify the voltage response as a vector.
Set up the projector parameters, and obtain the voltage response at 45° azimuth and 30° elevation. Compute the responses at signal frequencies of 2, 5, and 7 kHz.
projector = phased.IsotropicProjector('FrequencyRange',[1 10]*1e3, ... 'VoltageResponse',[90 95 100 95 90]); fc = [2e3 5e3 7e3]; resp = projector(fc,[45;30]); resp
resp = 1×3 0.0426 0.0903 0.0708
Next, draw a 2-D plot of the voltage response as a function of azimuth
pattern(projector,fc,[-180:180],0,'CoordinateSystem','rectangular', ... 'Type','power')
Directivity describes the directionality of the radiation pattern of a sensor element or array of sensor elements.
Higher directivity is desired when you want to transmit more radiation in a specific direction. Directivity is the ratio of the transmitted radiant intensity in a specified direction to the radiant intensity transmitted by an isotropic radiator with the same total transmitted power
where Urad(θ,φ) is the radiant intensity of a transmitter in the direction (θ,φ) and Ptotal is the total power transmitted by an isotropic radiator. For a receiving element or array, directivity measures the sensitivity toward radiation arriving from a specific direction. The principle of reciprocity shows that the directivity of an element or array used for reception equals the directivity of the same element or array used for transmission. When converted to decibels, the directivity is denoted as dBi. For information on directivity, read the notes on Element Directivity and Array Directivity.
Computing directivity requires integrating the far-field transmitted radiant intensity over all directions in space to obtain the total transmitted power. There is a difference between how that integration is performed when Antenna Toolbox™ antennas are used in a phased array and when Phased Array System Toolbox™ antennas are used. When an array contains Antenna Toolbox antennas, the directivity computation is performed using a triangular mesh created from 500 regularly spaced points over a sphere. For Phased Array System Toolbox antennas, the integration uses a uniform rectangular mesh of points spaced 1° apart in azimuth and elevation over a sphere. There may be significant differences in computed directivity, especially for large arrays.